Leo Varadkar. The row over the border erupted after his transport minister said he ‘would anticipate that there would be checks’.
Photograph: Brian Lawless/PA

Ireland’s prime minister has denied having secret plans to introduce checks at the border with Northern Ireland in the event of a no-deal Brexit.

Leo Varadkar was accused by the leader of Ireland’s opposition of keeping plans from voters after his deputy was overheard telling his transport minister he should avoid talking about checks on the border.

“It seems there is a private understanding and knowledge of a border in the aftermath of a no-deal Brexit but at all costs that private understanding must not be shared with the public,” said the Fianna Fáil leader, Micheál Martin, during leaders’ questions in the Dáil.

“It’s like the scene in Fawlty Towers: ‘Whatever you do don’t mention the war,’” added Martin, whose party is supporting Varadkar’s Fine Gael in a confidence and supply deal similar to Theresa May’s deal with the DUP.

The row over border checks erupted after the transport minister, Shane Ross, told reporters at a press conference after May’s Commons defeat on Tuesday he “would anticipate that there would be checks” on lorries coming from Scotland to the Republic of Ireland via Northern Ireland.

In an unguarded comment caught on microphone after the press conference, he asked Simon Coveney, the deputy prime minister, whether he should have made the remark.

Coveney replied: “Yes, but we can’t get into where they’ll be at this stage. They could be in the sea, they could be … But once you start talking about checks anywhere near the border, people will start delving into that and all of a sudden we’ll be the government that reintroduced a physical border on the island of Ireland.”

Ross responded: “Yeah, but I didn’t know what to say.”

Coming under pressure during leaders’ questions, Varadkar said: “We are not planning for checks on the land border in Northern Ireland.”

All Coveney’s remarks proved, he said, is “that if you use the wrong words, or you say things in the wrong way, people will misinterpret that as meaning a secret plan and there is no such secret plan”.

“We had a hard border between Ireland and Northern Ireland. I remember it well during the Troubles … and before the single market in 1993,” he said. “I remember going there as a teenager. I remember the customs checks, I remember the 24-hour rule, I remember seeing soldiers, and I never want to see any of that ever again.”

Pressed on how the government could possibly avoid mandatory checks on the border to protect the single market, Varadkar said that was for Brexiters who voted against May’s deal to sort out.

Hitting out at Conservative MPs such as Owen Paterson, Jacob Rees-Mogg and Boris Johnson who say the border issue is a fiction, he said: “It’s not good enough for those who rejected that to say there isn’t going to be a hard border because everyone says [so].

“The only way we can avoid a hard border between Ireland and Northern Ireland is having an agreement on customs, common customs union and regulatory alignment and that’s what we negotiated in the withdrawal agreement and the backstop.”

“We have come up with the solution, we have it in the agreement,” he said, adding that if Westminster opted for no deal it would still have to honour the border promises.

“It is now for those who rejected that to honour their commitment to us that there will be no hard border in island of Ireland – the ball is very much in their court,” Varadkar continued. “I don’t think they will be able to come up with a solution very different [to the withdrawal agreement].”

His remarks come after the DUP leader, Arlene Foster, also claimed the border fears were exaggerated and that Ireland was refusing to come up with a solution.

“For those of us who lived on the border and who were attacked by the IRA, we know that the IRA escaped across that border, so it was not a hard border, nobody wants to go back to that,” she told U105.8 FM radio.

“It takes the will to look for solutions and the regrettable thing is the Republic of Ireland has not been in the solution-finding mode.”